Exponent rules : (a^m)^n = a^(mn) and a^0 = 1
(4^9)^5 * 4^0 =
4^45 * 1 =
4^45 <==
Givens
sin(2x) = 2 * sin(x) * cos(x)
Equation
sin(x)*sin2(X) = 2sin(x) * 2sin(x)*cos(x) = 1
4*sin^2(x)* cos(x) = 1
sin^2(x) = 1 - cos^2(x)
4(1 - cos^2(x) ) * cos(x) = 1 Divide by 4
(1 - cos(x) ) *cos(x) = 1/4
cos(x) - cos^3(x) = 1/4
Let y = cos(x)
y - y^3 = 1/4
This is a cubic. I have to use a calculator's built in formula to solve it.
a = -1
b = 0
c = 1
d = - 1/4
Solution
y1 = - 1.107. Extraneous cos(x) can't be less than 1.
y2 = 0.8376
y3 = 0.2696
but cos(x) = y
cos-1(0.8376) = 33.11 degrees.
cos-1(0.2696) = 74.36 degrees.
The cosine is also plus in quad 4.
x = 360 - 33.11 = 326.89
x = 360 - 74.36 = 285.64
The graph of the cubic is below. It pretty much confirms what I found.
Answer:
hablan español es que yo les pudiera ayudar pero no se tanto ingles como ustedes
This is a good example of a problem that is being used to trip you up! haha
Think it through like this.
Proportional to up is up and proportional to down is down.
Is the elevator going up? Yes
Is the time to get to a floor going up the higher it goes? Yes.
So the 750 feet means nothing in this problem.
The simple answer is yes.